Strain-Engineered Electronic Structure and Superconductivity in La$_3$Ni$_2$O$_7$ Thin Films

Recently, the films of the Ruddlesden-Popper (RP) nickelate superconductors, in which the (La,Pr)$_3$Ni$_2$O$_7$ system exhibits a remarkable transition temperature $T_c$ exceeding 40 K, were synthesized at ambient pressure. We systematically investigate the band structures and electronic correlation effect to identify the key factors controlling superconductivity and pathways to enhance $T_c$. Based on density functional theory (DFT) calculations, we construct a bilayer two-orbital ($3d_{3z^2-r^2}$ and $3d_{x^2-y^2}$) tight-binding model for a series of in-plane compression mimicking the substrate effect. We find the band energy at the $M$ point drops with the compression, leading to increase of the density of states at the Fermi level, in stark contrast to the behavior of the bulk under pressure. We then apply functional renormalization group (FRG) method to study the electronic correlation effect on the superconductivity. We find the $s_\pm$-wave pairing symmetry remains robust in the films, the same as the bulk. But somewhat surprisingly, for the films, we find $T_c$ can be enhanced by reducing the in-plane lattice constant, increasing the out-of-plane lattice constant, or further electron-doping. These findings are consistent with the itinerant picture of the superconductivity induced by spin-fluctuations and provide theoretical support for further boosting $T_c$ in future experiments.